Orbital Dynamics of the Earth-Moon System

Gravity, which can be described as a central force, is a significant factor governing celestial phenomena such as the orbital motion of planets, stars, and galaxies. Careful study of orbital dynamics may even be used to find indirect evidence of black holes. The mathematical form given to Kepler’s laws by Isaac Newton allows the prediction of many properties of these orbits, where it finds continued relevance.

The purpose of this project is to 1) Model the orbital dynamics of the Earth-Moon system 2) Represent such orbital motion graphically 3) Verify the theoretical predictions of such orbit with experimental data from NASA.

The equations of motion will be obtained using both Newtonian Analysis and Lagrangian Dynamics, for 1) the Moon’s orbit, taking the Earth as fixed, 2) the barycentric motion of the Moon and the Earth. This technique tied to reduced mass, includes the determination of the center of mass (com)

of the Earth-Moon system as well as the eccentricity of their respective orbits. All utilized methods will be plotted graphically via Matlab/Octave and compared with experimental data.

Both the Newtonian and Lagrangian methods lead to the same equations of motion. As anticipated, the inclusion of the reduced and center of mass concepts increase the accuracy of both moon and earth orbital motions, based on their comparison with experimental data.